A student struggles to isolate terms in a kinematics equation. To express the formula
in terms of acceleration, Doctor Ian suggests substituting; then points out its quadratic
nature to solve it with respect to time.

Why is it that when you multiply or divide two numbers or variables
they become one term (such as 2*x becoming 2x), but when you add or
subtract two numbers or variables they are still two terms (such as 2
+ x)?

What are the official, mathematical names for polynomials with more
than three terms? For example, a polynomial with one term is a
monomial, with two terms is a binomial, and with three terms is a
trinomial. What is a polynomial with more than three terms called?

An algebra teacher wonders how to explain the existence of negative polynomial
remainders to students accustomed to positive remainders. Doctor Peterson clarifies
the difference between the remainders of arithmetic and those of algebra,
underscoring polynomial degree.